Program families: Program construction by context independent refinements

Abstract

The concept of program families is a generalisation of the conventional stepwise refinement paradigm. We formalise program families by allowing Hoare-triplets to be parameterized. Next we derive a simple calculus to develop programs which are known a priori to be correct with respect to explicitly formulated pre- and postconditions. Program families deal with at least two important problems of conventional refinement steps, i.e. program families are not context dependent and they apply just as well to top-down decomposition as to the bottom-up or middle-out approach. It turns out that the meaning of a pseudostatement in the context of program families is quite different from its meaning in the conventional refinement process. A couple of examples illustrate the technique: the 1000 primes problem, a palindrome filter and a sorting routine. The discussion relates program families to Morgan's refinement calculus, Knuth' literate programming and Soloway's programming plans.